Background : Leach’s storm-petrels (Hydrobates leucorhous)

Background: Pre-breeding Behaviour in Seabirds

Example: Common Terns (Sterna hirundo) move between colonies (Dittman et. al. 2005, 2007)

Background: Study Site

Questions:

  • Do sub-adult Leach’s storm-petrels attend multiple breeding colonies?

  • Do they visit the same colony multiple times?

  • Can we identify characteristics of individuals that predict colony attendance behaviour?

Quick initial results: Questions 1 & 2

Methods: VHF Tracking Primer

Methods: VHF Tracking Primer

Pros:

  • Tags are lightweight, long-lived and relatively inexpensive
  • All data is received and stored by receivers, so tags never need to be retrieved
  • Reliable for presence/absence, provides some data on distance/direction of animal

Limitations

  • Triangulating animals’ exact positions impossible*
  • Data coverage is restricted to the reception area of the receiving station; no data from animals outside that range

Methods: Capturing Birds and Identifying Sub-adults

Methods: Capturing Birds and Identifying Sub-adults cont.

Data Structure

All captured birds (n = 245):

All tagged birds (n = 28):

  • sex (pending)
  • number of return visits and number of islands visited

Data structure cont.

VHF data:

  • Nighttime light levels (pending)
  • Weather conditions (pending)

Data Structure cont.

Model 1: Morphology

Variables of Interest:

Variable Symbol Type Role Factor Type
Returned R Binomial Response NA
Wing chord WC Ratio Explanatory Fixed
Weight WT Ratio Explanatory Fixed

Model 1: Morphology

Graphical Model

Model 1: Morphology

Formal Model

\[ R = \beta_0 + \beta_{WC}WC + \beta_{WT}WT + \beta_{WC * WT}WC*WT + \epsilon \] Degrees of Freedom:

\[ 28 = 1 + 1 + 1 + (1)(1) + 24 \]

Model 1: Morphology

Fit Model

morphology_model <- glm(data = banding_data, R ~ weight+wing_chord+weight*wing_chord, family = binomial(link="logit"))

anova(morphology_model)
Analysis of Deviance Table

Model: binomial, link: logit

Response: R

Terms added sequentially (first to last)

                  Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL                                 27     35.165         
weight             1  0.06554        26     35.099   0.7979
wing_chord         1  0.34723        25     34.752   0.5557
weight:wing_chord  1  0.60330        24     34.149   0.4373

The interaction term appears trivial, so we can drop it and re-write the model:

\[ R = \beta_0 + \beta_{WC}WC + \beta_{WT}WT + \epsilon \]

Model 1: Morphology

Evaluate Model

Model 1: Morphology

Is a Quasi-binomial distribution any better?

Not really.

Model 1: Morphology

Evaluate Evidence

anova(morphology_model)
Analysis of Deviance Table

Model: binomial, link: logit

Response: R

Terms added sequentially (first to last)

                  Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL                                 27     35.165         
weight             1  0.06554        26     35.099   0.7979
wing_chord         1  0.34723        25     34.752   0.5557
weight:wing_chord  1  0.60330        24     34.149   0.4373

\[ G = \Delta Deviance \]

\[ LR = e^{G/2} \]

\[ LR = e^{1.016/2} \] \[ LR = 1.662 \]

Not convincing! There isn’t compelling evidence that morphology had an effect on whether or not tagged birds returned.

Model 2: Handling

Variables of Interest

Variable Symbol Type Role Factor Type
Returned R Binomial Response NA
Handling Time HT Ratio Explanatory Fixed
Second Handler (HA, DW, or SW) HA Nominal Explanatory Random

Model 2: Handling

Graphical Model

Model 2: Handling

Formal Model

\[ R = \beta_0 + \beta_{HT}HT + \beta_{HA}HA + \beta_{HT * HA}HT * HA + \epsilon \]

Degrees of Freedom

\[ 28 = 1 + (3-1) + (1)(3-1) + 23 \]

Model 2: Handling

Fit Model

banding_data <- banding_data %>% 
  mutate(handling_time = as.numeric(handling_time))


handling_glm <- glm(data = banding_data, R ~ handling_time + second_handler + handling_time*second_handler, family = binomial(link="logit"))

Model 2: Handling

Evaluate Model

Model 2: Handling

Is Quasi-binomial any better?

Again, not really.

Model 2: Handling

Evaluate Evidence

anova(handling_glm)
Analysis of Deviance Table

Model: binomial, link: logit

Response: R

Terms added sequentially (first to last)

                             Df Deviance Resid. Df Resid. Dev Pr(>Chi)   
NULL                                            27     35.165            
handling_time                 1   0.5688        26     34.596 0.450745   
second_handler                2   3.0734        24     31.523 0.215089   
handling_time:second_handler  2  12.8555        22     18.667 0.001616 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

A significant interaction effect!

Handler likely has an effect on handling time; not a surprise.

I am mainly interested in handling time, so I’ll assess that on its own.

Model 2: Handling

Handling time only

Model 2: Handling Time

Evaluate Evidence

Analysis of Deviance Table

Model: binomial, link: logit

Response: R

Terms added sequentially (first to last)

              Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL                             27     35.165         
handling_time  1  0.56878        26     34.596   0.4507

\[ LR = 1.329 \]

There is not compelling evidence that handling time affected whether or not a tagged bird returned.

Model 3: Island of Capture

Variables of Interest

Variable Symbol Type Role Factor Type
Returned R Binomial Response NA
Island of Capture (Great or Gull) Is Nominal Explanatory Fixed

Model 3: Island of Capture

Graphical Model

Model 3: Island of Capture

Formal Model

\[ R = \beta_0 + \beta_{Is}Is + \epsilon \]

Degrees of Freedom:

\[ 28 = 1 + (2-1) + 26 \]

Model 3: Island of Capture

Fit Model

island_glm <- glm(data = banding_data, R~location, family=binomial(link="logit"))

Model 3: Island of Capture

Evaluate Model

Weird!

Model 3: Island of Capture

Quasi-binomial?

Again, not much better.

Model 3: Island of Capture

Evaluate Evidence

Analysis of Deviance Table

Model: binomial, link: logit

Response: R

Terms added sequentially (first to last)

         Df Deviance Resid. Df Resid. Dev Pr(>Chi)
NULL                        27     35.165         
location  1   2.2078        26     32.957   0.1373

\[ LR = 3.0162 \]

There is not convincing evidence that island of capture affected whether tagged birds returned.

(if anyone is interested, if you set this up as a classic Chi-squared test, the p-value is 0.09.)

Questions?

Acknowledgements

  • Project supervised by David Wilson

  • Environment & Climate Change Canada (especially Dave Fifield and Sabina Wilhelm) graciously allowed us to use their VHF receivers

  • Fieldwork help & Photography: Kobe Loveless, Hallie Arno, Sabina Wilhelm, Chris Ward, Gill Holmes

  • Project funding from NSERC Discovery Grant to Dr. Wilson